00:01
For this problem, to begin, we know that we have that the probability of event a occurs is 1 over 3.
00:08
Probability that b occurs, given a, is equal to 1 over 4.
00:15
And we have that the probability of not a or a complement and not b or b complement is equal to 1 over 6.
00:25
And we're asked to find probability of b.
00:30
Now, one thing that i'll note here is that probability of not a and not b is the same thing as the probability of not a or b, which in turn would be equal to 1 minus the probability of a or b.
00:53
So if probability of not a or b is 1 over 6, then that means that probability of a or b is equal to 5 over 6.
01:03
You should recall that probability of a or b would be equal to probability of a plus probability of b minus the probability of a and b.
01:23
Probability of a and b can be calculated as probability of b given a times p of a.
01:31
And at this point, we can rearrange this formula to get p of b just in terms of things that we know.
01:37
So we have probability of event b will be equal to probability of a or b plus probability of b given a times p of a minus p of a.
02:00
Probability of a or b was 5 over 6.
02:04
Probability of b given a is 1 over 4.
02:06
Probability of a is 1 over 3.
02:09
And we then subtract probability of a, which is 1 over 3.
02:13
Which gives us a result of 7 over 12.
02:20
And then for the second part of the problem there, we're told that we have a third event c, is such that a and c are independent, with p of a and c is 1 over 36, which i'll note is equal to p of a times p of c, since we know that a and c are independent.
02:47
And we have that probability of b or c is equal to 2 over 3, which in turn would have to be probability of b plus probability of c, minus probability of a and c.
03:05
We know what probability of b is...